Base Calculator

A number base, or radix, is the number of unique digits used to represent numbers in a positional numeral system. Base 10 (decimal) uses digits 0–9, while Base 2 (binary) uses only 0 and 1. Bases above 10 use letters — for example, Base 16 (hexadecimal) uses digits 0–9 and letters A–F. See also our calculate Binary (Base 2), Octal (Base 8) & Hexadecimal (Base 16) — Decimal to Binary Converter.

The easiest method is to convert each number to decimal first, perform the addition, then convert the result back to the target base. Alternatively, you can add directly in the target base by carrying values based on that base — for example, in binary (base 2), 1 + 1 = 10 (carry the 1). This calculator handles both conversions automatically.

For bases above 10, letters extend the digit set. Base 11 adds 'A' (value 10), Base 12 adds 'A' and 'B', and so on up to Base 36, which uses digits 0–9 and letters A–Z. This calculator accepts uppercase or lowercase letters as input.

Computers use binary because electronic circuits have two reliable states — on (1) and off (0). This makes binary the natural language of digital hardware. All data, instructions, and calculations inside a computer are ultimately represented as sequences of 1s and 0s. You might also find our calculate Octal to Decimal Converter Decimal Value (Base-10) useful.

Hexadecimal is widely used in programming, web design (color codes like #1e3a5f), and memory addressing because it compactly represents binary data — each hex digit corresponds to exactly 4 binary bits. It makes long binary strings much easier to read and write.

Yes. Enter both numbers in your chosen base, select ÷ as the operation, and the calculator will convert both numbers to decimal, perform the division, and return the result converted back to your selected base. Note that division may produce a decimal (fractional) result; this calculator returns the integer portion.

Octal was historically used in computing because it maps neatly to binary — each octal digit represents 3 binary bits. It was common in early Unix file permission notation (e.g. chmod 755) and older computer systems, though hexadecimal has largely replaced it in modern usage.

The standard approach is to use decimal (base 10) as an intermediate. Convert the original number to decimal, then convert from decimal to the target base by repeatedly dividing by the target base and recording remainders. This calculator automatically displays the result in binary, octal, decimal, and hexadecimal so you can see all four representations at once.